Transition Functions of Diffusion Processes on the Thoma Simplex

Korotkikh, Sergei

doi:10.1134/s0016266320020057

Cited by 1 publication

(8 citation statements)

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“…Therefore, similar to the Ewens sampling formula, we have and . Then, we can easily see that (6) is equivalent to the density in [11].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 90%

“…By spectral expansion of in the Hilbert space , the following explicit transition density of was obtained in [11].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

“…In [11], it was shown that By the following Proposition 2, [2] showed that the representing measure of the Z partition structure is the Z -measure .…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

“…Due to the estimation of in [11], the proof of Theorem 1 is the same as the proof of [17, Theorem 2.1].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

“…Recently, spectral expansion was again applied to the Z -measure diffusion in [11] to derive its explicit transition density. A similar method was previously used to establish the transition density of the two-parameter Poisson–Dirichlet diffusion in [6].…”

Section: Introductionmentioning

confidence: 99%

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Transition density of an infinite-dimensional diffusion with the jack parameter

Zhou

2023

J. Appl. Probab.

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From the Poisson–Dirichlet diffusions to the Z-measure diffusions, they all have explicit transition densities. We show that the transition densities of the Z-measure diffusions can also be expressed as a mixture of a sequence of probability measures on the Thoma simplex. The coefficients are the same as the coefficients in the Poisson–Dirichlet diffusions. This fact will be uncovered by a dual process method in a special case where the Z-measure diffusions are established through an up–down chain in the Young graph.

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“…Therefore, similar to the Ewens sampling formula, we have and . Then, we can easily see that (6) is equivalent to the density in [11].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 90%

“…By spectral expansion of in the Hilbert space , the following explicit transition density of was obtained in [11].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

“…In [11], it was shown that By the following Proposition 2, [2] showed that the representing measure of the Z partition structure is the Z -measure .…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

“…Due to the estimation of in [11], the proof of Theorem 1 is the same as the proof of [17, Theorem 2.1].…”

Section: The Z-measure Diffusion and Its Transition Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations